Question

Solve the given set of equations by applying L-U decomposition method. The upper triangular matrix U should include 1's on its diagonal. 1.5x1+2.4x2-2.1x3=-1.86 2.4x1+7.04x2-0.16x3=-2.656 1.4x1+3.44x2-3.16x3=-4.496 

          Solve the given set of equations by applying L-U decomposition method. The upper triangular matrix U should include 1's on its diagonal.
1.5x1+2.4x2-2.1x3=-1.86
2.4x1+7.04x2-0.16x3=-2.656
1.4x1+3.44x2-3.16x3=-4.496
Solve the given set of equations by applying L-U decomposition method. The upper triangular matrix U should include 1's on its diagonal. 1.5x1+2.4x2-2.1x3=-1.86 2.4x1+7.04x2-0.16x3=-2.656 1.4x1+3.44x2-3.16x3=-4.496

Added by Edward C.

Close

University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
AceChat toggle button
Close icon
Ace pointing down

Please give Ace some feedback

Your feedback will help us improve your experience

Thumb up icon Thumb down icon
Thanks for your feedback!
Profile picture
Solve the given set of equations by applying LU decomposition method. The upper triangular matrix U should include 1's on its diagonal. 1.5x + 2.4x^2 - 2.1x^3 = -1.86 2.4x + 7.04x^2 - 0.16x^3 = -2.656 1.4 + 3.44x^2 - 3.16x^3 = -4.496
Close icon
Play audio
Feedback
Powered by NumerAI
David Collins Ivan Kochetkov
Danielle Fairburn verified

Adi S and 72 other subject Physics 101 Mechanics educators are ready to help you.

Ask a new question
*

Labs

-

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs
*

Key Concepts

-
Key Concept
Premium Feature
Explore the core concept behind this problem.
Play button
Key Concept
Premium Feature
Explore the core concept behind this problem.
Your browser does not support the video tag.
*

Recommended Videos

-
given-the-linear-system-x1-2x2-4x3x4-13-2x1-xz-3x3-2x4-16-3x1-xz-xz-2x4-5-x1-3x2-x3-x4-7-a-factor-the-coefficient-matrices-into-the-lu-decomposition-using-the-lu-factorization-algorithm-with-01903

Given the linear system x1 + 2x2 + 4x3 + x4 = 13 2x1 - x2 + 3x3 + 2x4 = 16 3x1 + x2 - x3 - 2x4 = -5 x1 + 3x2 - x3 - x4 = -7 (a) Factor the coefficient matrices into the LU decomposition using the LU Factorization Algorithm with l_ii = 1 for all i. (b) Use LU decomposition to solve the linear system.

Adi S.
find-the-matrix-of-the-quadratic-form-assume-mathbfx-is-in-mathbbr3-a-3-x_12-2-x_225-x_324-x_1-x_2-6

Find the matrix of the quadratic form. Assume $\mathbf{x}$ is in $\mathbb{R}^{3}$ . a. $3 x_{1}^{2}-2 x_{2}^{2}+5 x_{3}^{2}+4 x_{1} x_{2}-6 x_{1} x_{3}$ b. $4 x_{3}^{2}-2 x_{1} x_{2}+4 x_{2} x_{3}$

Linear Algebra and Its Applications

Symmetric Matrices and Quadratic Forms

Quadratic Forms
solve-the-system-by-inverting-the-coefficient-matrix-and-using-theorem-16-2-beginarrayrr-x_13-x_2x_3

Solve the system by inverting the coefficient matrix and using Theorem $1.6 .2 .$ $$\begin{array}{rr} x_{1}+3 x_{2}+x_{3}= & 4 \\ 2 x_{1}+2 x_{2}+x_{3}= & -1 \\ 2 x_{1}+3 x_{2}+x_{3}= & 3 \end{array}$$

Elementary Linear Algebra: Applications Version

Systems of Linear Equations and Matrices

More on Linear Systems and Invertible Matrices
*

Recommended Textbooks

-
University Physics with Modern Physics

University Physics with Modern Physics

Hugh D. Young 14th Edition
achievement 1,580 solutions
Physics: Principles with Applications

Physics: Principles with Applications

Douglas C. Giancoli 7th Edition
achievement 1,228 solutions
Fundamentals of Physics

Fundamentals of Physics

David Halliday, Robert Resnick , Jearl Walker 10th Edition
achievement 1,101 solutions
*

Transcript

-
00:01 In this question we have been given a linear system we have to factor the coefficient matrices into lu decomposition with lii is equals to 1 this is for all i so we will write the given system in the form of ax equals to b where a is the coefficient matrix so i will write the matrix as 1 2 4 1 i am not writing the equation here you can refer to the questions this is 2 minus 2 minus 1 3 2 then we have 3 1 minus 1 minus 2 1 3 minus 1 minus 1 since we have to factorize it i will let a is equals to lu where we know that l is a lower triangular matrix so i will get on the diagonal everywhere it is 1 and above it we have zeros everywhere and this will be l 2 1 l 3 1 l 3 2 this is l 4 1 l 4 2 l 4 3 lii is equals to 1 that means each of the diagonal entries is 1 and then we write the upper triangular matrix u11 u12 u13 u14 next is 0 u22 u23 u24 then 0 0 u33 u34 and here everywhere 0 this will be u44 so this is how we write a is equals to lu now if i multiply and compare multiply and compare both sides what we are going to get is following things u11 equals to 1 u12 comes out to be equal to 2 u13 is equals to 4 and u14 we get as minus 1 so this is if we compare row r1 next if i compare row r2 that is a second row on both the side i will get l 2 1 u11 equals to 2 u11 will know from that we get l 2 1 equals to 2 similarly i will get l 2 1 u12 plus u22 equals to minus 1 which implies l u22 will be minus 5 next is l 2 1 times u13 plus u23 i get it to be 3 which implies u23 is equals to minus 5 also i get that u14 times l 2 1 plus u24 equals to 2 which implies…
Need help? Use Ace
Ace is your personal tutor. It breaks down any question with clear steps so you can learn.
Start Using Ace
Ace is your personal tutor for learning
Step-by-step explanations
Instant summaries
Summarize YouTube videos
Understand textbook images or PDFs
Study tools like quizzes and flashcards
Listen to your notes as a podcast
Continue solving this problem
Create a free account to:
  • View full step-by-step solution
  • Ask follow-up questions with Ace AI
  • Save progress and study later
Continue Free
Numerade

Get step-by-step video solution
from top educators

Continue with Clever
or



By creating an account, you agree to the Terms of Service and Privacy Policy
Already have an account? Log In

A free answer
just for you

Watch the video solution with this free unlock.

Numerade

Log in to watch this video
...and 100,000,000 more!


EMAIL

PASSWORD

OR
Continue with Clever